Why are my model's clothes collapsing in on itself?
The simplest solution is to remove the inner faces of the clothing model, since they should never be seen when worn on a character. In game development, its in your best interest to exclude any faces of a model that will never be seen, so you don't bog down your frame rate with excess geometry.

If you absolutely must keep the inner faces of cloth on your character for whatever reason, then your issue exists in the outer vertices of the cloth having more or less influence than the inner vertices. You'll want to improve your vertex weights to accomodate the thin thickness of the cloth.